On Reconstructability of Quadratic Utility Functions from the Iterations in Gradient Methods

Farhad Farokhi; Iman Shames; Michael G. Rabbat; Mikael Johansson

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arXiv · 1509.05500

On Reconstructability of Quadratic Utility Functions from the Iterations in Gradient Methods

Farhad Farokhi·Iman Shames·Michael G. Rabbat·Mikael Johansson

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Abstract

In this paper, we consider a scenario where an eavesdropper can read the content of messages transmitted over a network. The nodes in the network are running a gradient algorithm to optimize a quadratic utility function where such a utility optimization is a part of a decision making process by an administrator. We are interested in understanding the conditions under which the eavesdropper can reconstruct the utility function or a scaled version of it and, as a result, gain insight into the decision-making process. We establish that if the parameter of the gradient algorithm, i.e.,~the step size, is chosen appropriately, the task of reconstruction becomes practically impossible for a class of Bayesian filters with uniform priors. We establish what step-size rules should be employed to ensure this.

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Farhad Farokhi, Iman Shames, Michael G. Rabbat, Mikael Johansson. 2015-09-18. On Reconstructability of Quadratic Utility Functions from the Iterations in Gradient Methods. https://arxiv.org/abs/1509.05500

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